Question

The radius of the earth is r. at what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2? the radius of the earth is . at what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2? 0.50r 0.41r 2.0r 1.0r 1.4r

Answer 1

The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s^2?
A) 0.41R
B) 0.50R
C) 1.0R
D) 1.4R
E) 2.0R
A

Answer 2

Answer:

Height will be 0.41 r

Explanation:

We have given acceleration due to gravity at any height is $g_{new}=4.9m/sec^2$

Radius of the earth = r

We know that acceleration due to gravity at any height is given by

$g'=\frac{GM}{(R+h)^2}$----eqn 1

And acceleration due to gravity at earth $g=\frac{GM}{R^2}$----eqn2

Dividing eqn 2 by eqn 1

$\frac{g}{g'}=\frac{(r+h)^2}{r^2}$

$\frac{9.8}{4.9}=\frac{(r+h)^2}{r^2}$

$2r^2=(r+h)^2$

$\sqrt{2}r=h+r$

h = 0.41 r